Bounds of the Möbius inverse of monotone set functions

We give the upper and lower bounds of the Möbius inverse of monotone and normalized set functions (a.k.a. normalized capacities) on a finite set of n elements. We find that the absolute value of the bounds tend to 4 n/2 √ πn/2 when n is large. We establish also the bounds of the interaction transform and Banzhaf interaction transform, as well as the bounds of the Möbius inverse for the subfamilies of kadditive normalized capacities and p-symmetric normalized capacities.